Answer:
Step-by-step explanation:
<u>Statements </u> <u> Reasons</u>
1) QS =42 Given
2) QR + RS = QS Segment Addition Postulate
3) (x + 3) + 2x = 42 Substitution Property
4) 3x + 3 = 42 Simplify
5) 3x = 39 Subtraction Property of Equality
6) x=13 Division Property of Equality
Explanation:
We have given QS=42. We have to prove that x=13
We will use Segment Addition Postulate which states that given 2 points Q and S, a third point R lies on the line segment QS if and only if the distances between the points satisfy the equation QR + RS = QS.
Then we will substitute the values in the defined postulate.
where QR= x+3
RS=2x
QS=42
QR+RS=QS
(x+3)+2x= 42
Now simplify the expression by opening the brackets.
x+3+2x=42
3x+3=42
Now subtract 3 from both sides.
3x+3-3=42-3
3x=39
divide both sides by 3.
3x/3 =39/3
x=13..
Fourth option has the same y-intercept of (0,3) as the sample above.
y+3=6x
it equals to y=6x-3
Answer:
QR = 12 (cm), RP = 10 (cm)
Step-by-step explanation:
Corresponding sides of the triangles:
XY : PQ, YZ : QR, ZX : RP.
For similar triangles ratios of corresponding sides are the same
XY : PQ = 4 : 8 = 1 : 2
YZ : QR = 1 : 2
ZX : RP = 1 : 2
YZ : QR = 1 : 2
6 : QR = 1 :2, QR = 12 (cm)
ZX : RP = 1 : 2
5 : RP = 1 : 2, RP = 10 (cm)
Answer:
y=1/2x-2
Step-by-step explanation:
perpendicular lines have a neg. reciprocal for the slope.
for example:
in this equation y=-2x+1
-2 is the slope and the negative reciprocal would be 1/2
hence, the slop of our new line is 1/2
y=1/2x+b
we can substitute the coordinates given for x and y:
2=1/2(8)+b
2=4+b
-2=b
hence the new equation is y=1/2x-2
To solve for variable h flip the equation. You get: 12gh=f. After, divide both sides by 12 to get your answer: h=f/12g
